Preheat the oven to 180C/350F (fan). Separate the eggs, place the whites in a large mixing bowl and the yolks in a second mixing bowl.
Use an electric hand whisk to beat the egg whites for a couple of minutes until they form soft peaks of foam. Then, add the caster sugar to the beaten egg whites and whisk again for 3-5 minutes until you have stiff peaks of foam.
In the other bowl, beat the yolks together with the milk, until frothy, then add to the egg whites and sugar before whisking them together for a couple of minutes.
Sift the cocoa, flour and xanthan gum over the frothy mixture. Now use a spatula to fold the dry ingredients into the egg mixture, without knocking out all the air. Fold and scrape at a slow pace, until fully incorporated. The mixture should still be quite mousse-like and full of air.
Line a rectangular baking tray (mine is 32cm x 22cm) with greaseproof paper, so that the base and sides are covered. Pour the cake mixture onto the tray and gently spread to the sides and corners using a small palette knife. Bake at 180C/350F for 8-10 minutes, until cooked through - the sponge is thin so it cooks very quickly, and it's important that you don't overbake it as this will dry it out (and cause the sponge to crack when rolled).
Once baked, remove from the oven and allow to cool for 2 minutes. Then place a clean tea towel over the top of the sponge, followed by a wire rack or large chopping board. Flip carefully to invert the tray and then lift the tray off the sponge. Ease the baking paper away from the sides, then peel back the baking paper and remove from the sponge.
Time to roll the sponge - fold the edge of the tea towel over the shorter edge of the sponge and roll into a log shape, so the tea towel is on outside of the sponge. Set aside to cool completely, still rolled up.
When the sponge has cooled, make the filling and frosting. For the chocolate fudge frosting mix the softened butter and cocoa powder in a mixing bowl to make a smooth paste. Add the icing sugar and 2 tablespoons of milk and mix until smooth. You may or may not need the third tablespoon of milk, depending on how warm the room is - you are aiming for a fairly stiff yet spreadable consistency.
For the filling, whisk the mascarpone in a bowl to loosen it, then add the vanilla and sift the icing sugar and cocoa into the bowl. Mix in with a spatula or wooden spoon, then whisk again to combine. Finally add the double cream and beat for about a minute until you have a thick, stiff cream mixture. You may not need to beat it for that long, just until the cream is worked in and slightly whipped - too much whipping will make the filling too stiff. If you have any issues, add a little extra cream and carefully stir through to loosen.
Time to assemble the yule log! Carefully unroll the cooled sponge, then spread the mascarpone cream all over the inside. Now roll the sponge up quite tightly, until you have a lovely swirl of chocolate sponge and cream.
Transfer to your serving board. Give the chocolate fudge icing a good stir, then spread it onto the yule log, to cover it completely. Use a fork to create a bark effect in the icing then dust with icing sugar and serve!
